# Diffraction With A Single Slit And A Lens.

1. Dec 10, 2012

### chris_avfc

1. The problem statement, all variables and given/known data
Trying to find the number of diffraction maxima and the width of the whole pattern.
$\lambda = 500nm$
$b = 2.8μm$ (Slit Width)
$f = 100mm$
$r = 25mm$
$L = 25mm$ (Slit to Lens)

2. Relevant equations

I have the worked out the irradiance formula as:

$$I(\theta)=I_0 sin^2(\beta)/(\beta^2)$$

The conditions for minima

$$b sin\theta = m\lambda$$

Angular width of central fringe

$$\Delta\theta \approx 2\lambda/b$$

Width of central fringe

$$W \approx 2L\lambda/b$$

3. The attempt at a solution

As said I worked out the irradiance formula, and I think to find the width of the whole pattern you would do:

$(Fringe Width \times 2) + 1$

As then it accounts for the dark fringes as well, plus the one extra for the central.

As for working out the number of maxima, I would guess it would involve the condition for a minimum as it contains the order of diffraction.

What really throws me off though, is the lens, I'm not sure what that would do for the calculations.

2. Dec 16, 2012

### chris_avfc

Sorry to bump this, but does anybody have any idea?

3. Dec 30, 2012

### chris_avfc

Going to be a pain and see if anyone can help me again?

Can't get anywhere with this. :(